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Symmetric informationally complete positive-operator-valued measures: A new computer study
We report on a new computer study of the existence of d2 equiangular lines in d complex dimensions. Such maximal complex projective codes are conjectured to exist in all finite dimensions and are the
On self-dual MDS codes
TLDR
It is shown that for q = 2<sup>m</sup>, there are self-dual MDS codes for all even lengths up to 2-m and for all odd prime powers q, there areSelf-duals of length q + 1 over F<sub>q</sub> exist.
SIC-POVMs: A new computer study
We report on a new computer study into the existence of d2 equiangular lines in d complex dimensions. Such maximal complex projective codes are conjectured to exist in all finite dimensions and are
Codes for the quantum erasure channel
TLDR
A family of quantum codes for the QEC, the quantum Bose-Chaudhuri-Hocquenghem codes, that can be efficiently decoded is introduced.
On SIC-POVMs and MUBs in Dimension 6
We provide a partial solution to the problem of constructing mutually unbiased bases (MUBs) and symmetric informationally complete POVMs (SIC-POVMs) in non-prime-power dimensions. An algebraic
Applying Grover's Algorithm to AES: Quantum Resource Estimates
TLDR
It is established that for all three variants of AES key size 128, 192, and 256i¾źbit that are standardized in FIPS-PUB 197, there are precise bounds for the number of qubits and thenumber of elementary logical quantum gates that are needed to implement Grover's quantum algorithm to extract the key from a small number of AES plaintext-ciphertext pairs.
On optimal quantum codes
TLDR
This work presents families of quantum error-correcting codes which are optimal in the sense that the minimum distance is maximal, and shows that codes with parameters 〚n, n - 2d + 2, d〛q exist for all 3≦n≤q and 1≤d≤n/2+1.
Convolutional and Tail-Biting Quantum Error-Correcting Codes
Rate-(n-2)/n unrestricted and CSS-type quantum convolutional codes with up to 4096 states and minimum distances up to 10 are constructed as stabilizer codes from classical self-orthogonal rate-1/n
Quantum information processing and communication
Abstract.We present an excerpt of the document “Quantum Information Processing and Communication: Strategic report on current status, visions and goals for research in Europe”, which has been
Quantum BCH Codes
TLDR
This work shows how to construct quantum error-correcting codes based on classical BCH codes, which can exploit additional information about the position of errors with this error model - the quantum erasure channel.
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